Equal or not?

Upon graphing the functions, they may appear the same. In fact they are exactly the same except for one value of $x$ . When $x=1$ in the first equation, there is no solution (you can't divide by zero) but there is a value for $x=1$ in the second equation. Both equations are similar, but it is a common misconception that they are the same thing.

Factorizing would cancel $x-1$ out, but since the first function is not defined with $x-1 = 0$ , then at $x = 1$ , this function will be discontinued and hence is not the same function to the latter.